Comparison of an Incremental Versus Single-Step Retraction Model for Intraoperative Compensation

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1 Comparison of an Incremental Versus Single-Step Retraction Model for Intraoperative Compensation L. A. Platenik a, M. I. Miga a, D. W. Roberts bc, F. E. Kennedy a, A. Hartov a, K. E. Lunn a, K. D. Paulsen abc a Thayer School of Engineering Dartmouth College, Hanover, NH USA b Dartmouth Hitchcock Medical Center Lebanon, NH USA c Norris Cotton Cancer Center Lebanon, NH USA ABSTRACT Distortion between the operating field and preoperative images increases as image-guided surgery progresses. Retraction is a typical early-stage event that causes significant tissue deformation, which can be modeled as an intraoperative compensation strategy. This study compares the predictive power of incremental versus single-step retraction models in the porcine brain. In vivo porcine experiments were conducted that involved implanting markers in the brain whose trajectories were tracked in CT scans following known incremental deformations induced by a retractor blade placed interhemispherically. Studies were performed using a 3-D consolidation model of brain deformation to investigate the relative predictive benefits of incremental versus single-step retraction simulations. The results show that both models capture greater than 75% of tissue loading due to retraction. We have found that the incremental approach outperforms the single-step method with an average improvement of 1.5% - 3%. More importantly it also preferentially recovers the directionality of movement, providing better correspondence to intraoperative surgical events. A new incremental approach to tissue retraction has been developed and shown to improve data-model match in retraction experiments in the porcine brain. Incremental retraction modeling is an improvement over previous single-step models, which does not incur additional computational overhead. Results in the porcine brain show that even when the overall displacement magnitudes between the two models are similar, directional trends of the displacement field are often significantly improved with the incremental method. Keywords: Image-Guided Neurosurgery, subsurface deformation, computational model, retraction 1. INTRODUCTION Since the implementation of stereotactic image-guidance into the field of neurosurgery, it has been observed that registration distortion between the operating field and preoperative images increases as surgery progresses. 1-7 Tissue movements resulting from intracranial pressure changes induced by craniotomy, dura removal, cerebrospinal fluid loss, and drug effects including blood volume manipulation cause errors in image registration performed at the start of surgery. 8,9 Continued fluid loss that contributes to time-dependent gravitational sag as well as surgical manipulation of tissue (i.e. retraction, resection) further negate the assumption that registration is fixed throughout the procedure Recent studies have been conducted to investigate the amount of brain shift that occurs during surgery, documenting surface deformations on the order of 0.5-2cm and subsurface motion up to 7mm. 14,16,20 In response to the need for improved accuracy and confidence during neuronavigation, several groups are working toward the implementation of non-rigid registration systems, including interventional magnetic resonance (imr), intraoperative ultrasonography (ius) and deformable models We have proposed a method to update preoperative images to the current state of the operating field using a computational model in conjunction with sparse intraoperatively acquired US and 3-D Correspondence: L. A. Platenik. leah.platenik@dartmouth.edu; Telephone: ; Fax: ; Supported by the National Institutes of Health (NIH) under Grant R01-NS33900 awarded by the National Institute of Neurological Disorders and Stroke. 358 Visualization, Display, and Image-Guided Procedures, Seong Ki Mun, Editor, Proceedings of SPIE Vol (2001) 2001 SPIE /01/$15.00

2 surface tracking data.33,35 An early study correlated clinically measured cortical shift to computational predictions of gravitational sag, with a significant improvement in registration error from 5.7 mm to 1.2 mm.10 After development of a porcine experimental system to quantify predictions, our goal to incorporate realistic surgical events (i.e. retraction and resection) into our model began with simulations of uniaxial loading, resulting in 75%-85% recovery of brain motion.34 We have recently developed a more sophisticated method of modeling surgical retraction which allows for the arbitrary orientation, placement and movement of a retractor within the mesh.38,39 This paper examines the comparison of two displacement methods with which we drive the computation and interpolate the solution. In vivo porcine experiments were conducted that involved implanting markers in the brain whose trajectories were tracked in CT scans following known incremental deformations induced by a retractor blade placed interhemispherically. Studies were performed to investigate the relative predictive benefits of incremental versus single-step retraction simulations. The results show that both models capture greater than 75% of tissue loading due to retraction. We have found that the incremental approach outperforms the single-step method with an average improvement of 2-4%. More importantly it also preferentially recovers the directionality of movement, providing better correspondence to intraoperative surgical events. 2. METHODS 2.1. In vivo experimental procedures Experiments were conducted on a series of four female subjects weighing between lbs. MR scanning was performed a priori. Following intubation and initiation of anesthesia, the subject was placed in a custom built stereotactic frame. A square region of skull centered above the frontal-parietal lobes was removed, leaving the dura temporarily intact. Markers, stainless steal 1mm beads, were inserted grid-wise into the parenchyma; markers were placed in the left hemisphere, corresponding to the hemisphere to be loaded while the remaining markers were mirror-implanted in the right hemisphere near the fissure. After fixation of the beads was determined by fluoroscopic imaging, the exposed dura mater covering the left hemisphere was removed in three of the four subjects, while the dura covering the entire craniotomy region was removed for subject 1. In line with beads, a retractor was mounted in a loading mechanism attached to the stereotactic frame. A picture of the apparatus can be seen in Figure 1. It was designed to impart uniaxial loading away from the midline by way of a user controlled lead-screw mechanism. Codman Microsensor ICP Transducers (Johnson & Johnson) were symmetrically placed around the retractor blade for interstitial pressure measurements which were recorded during deformation using a computer controlled data acquisition system and LABVIEW (National Instruments) software. Figure 1. (a) Experimental setup, (b) stereotactic frame illustrating loading mechanism. A CT image of the full skull was taken for mesh generation (3mm spacing). For the baseline scan and subsequent images, the scanning region was localized to the surgical focus with a slice spacing of 1mm. A CT scan was obtained following each retraction. Table 1 summarizes the measured blade displacements for each imparted load in each subject. Proc. SPIE Vol

3 Table 1. Measured retractions (mm), total (incremental). Retraction Step No. Subject #1 Subject #2 Subject #3 Subject #4 Average (3.9) 6.0 (3.3) 6.4 (3.2) 6.1 (2.9) 6.5 (3.3) (2.1) 8.0 (2.0) 8.2 (1.8) 8.2 (2.1) 8.5 (2.0) (2.1) na 9.9 (1.7) na 10.4 (1.9) 2.2. Computational model and mesh generation We have represented the brain as a biphasic porous medium consisting of a linearly elastic solid and an incompressible pore fluid. The following, adapted from 2-D consolidation physics 40 and work done by Nagashima et al. 41, are the governing equations describing the soft tissue mechanics in our model, G G u + ( u) α p = 0 1 2ν (1) 1 p α ( u) + κ p = 0 (2) t S t where G shear modulus (Pa); ν Poisson s Ratio; u displacement vector (m); p pore fluid pressure (Pa); α ratio of fluid volume extracted to volume change of the tissue under compression; κ hydraulic conductivity (m 3 s/kg); 1/S void compressibility constant (1/Pa). Equation (1) describes mechanical equilibrium and the mass conservation equation (2) relates volumetric strain to fluid drainage, where 1/S=0 and α=1; the pore is saturated with an incompressible fluid. The continuum equations are discretized using the method of weighted residuals and the system solved with the finite element method. The computational mesh boundary is generated by segmentation of the brain volume in computed tomographic (CT) image slices using Analyze AVW (Mayo Foundation). Custom software is employed to create a volumetric mesh with tetrahedral elements with increased discretization in the surgical region. 42 Voxel intensity thresholding of a coregistered MR image volume is used to extract white and gray mater patterns, allowing for heterogeneous application of material properties. Table 2 summarizes the model specifications and inputs as well as material property parameters. Table 2. Model properties. Material properties G=1kPa ν=0.46 κ(w)=1e-11, κ(g)=5e-12 Running properties t=60s, t f =300s θ=1 tolerance=1e-5 Mesh boundary properties linear triangular ~3500 nodes ~7500 elements 3-D mesh properties linear tetrahedral ~16500 nodes ~ elements 2.3. Retraction simulation methods and boundary conditions The initial location of the retractor blade is determined from the baseline CT image and the associated plane is incorporated into the mesh by splitting transected element vertices that are located along the path of the plane, 39 For each of the transected vertices, a coincident node is created and displaced a distance equal to the width of the retractor. The new nodes are independent from the parent nodes except at the junction of the split; creating two surfaces that represent tissue on the front 360 Proc. SPIE Vol. 4319

4 and back sides of the retractor. In the initial stages of loading, both surfaces are displaced normal to the retractor plane in accordance with the measured trajectory while at later stages the adherence of tissue to the back side is released, and the nodes are allowed to move freely, as observed in the CT data. This behavior in which the backside initially follows the front may be due to loose binding from blood clotting or expansion of tissue when a contiguous region is being removed. With each successive loading, the directional normal to the plane of the blade varies. In this study, the directional normal was taken to be that of the midsection of the blade. In the first compensation method, the single-step scheme, the solution for a retraction event was determined by driving the model by the total displacement using that step s final directional normal. For example, if we are considering retraction step #2 (~6mm), rather than using the baseline normal (at 0mm), we use the directional normal measured at the end of step #2 to drive the displacement corresponding to both steps #1 and #2 (3mm+3mm=6mm). This strategy allows some capture of the blade s trajectory rather than driving the model from the baseline normal for each step. In the second, or incremental retraction compensation method, each step, rather than the summation of the steps, is used to drive the model. The solution of the steps is then superimposed to obtain the final volumetric displacements. In this case, the directional normal of the blade measured prior to each step is used. The pressure induced at the surfaces of the blade is proportional to displacement by a previously determined calibration curve for the porcine brain. 43 The nodes lining the intracranial cavity are specified to be stress free only in the tangential direction, meaning they are allowed to slip along the walls of cranium. Above the region of the brainstem, no flux across this surface is allowed. In the region of the brainstem, the pressure is specified to equal zero, characterizing possible herniation that has been observed in that region. The remaining boundary conditions include those stress free nodes representing the region of exposed brain where the skull and dura have been removed including the nodes located astride the blade in the fissure, or split. The boundary conditions used are listed in mathematical form in Table 3 and pictured in Figure 2. Table 3. Mathematical description of boundary conditions. Boundary 1 (intracranial region, brainstem) σ (t)=0 δp/δn=0, p=0 Boundary 2 (loading region) U(n)=retractor displacement p(displacement)=calibration curve Boundary 3 (craniotomy, resected dura) σ (t)=0, σ (s)=0 δp/δn=0 Boundary 4 (internal structures at split juncture) U=0 δp/δn=0 1 3 Figure 2. Pictorial description of boundary conditions: (a) surface mesh depicting boundary regions 1 and 3, (b) nodal representation depicting boundary regions 2 (high density horizontal region) and 4 (high density vertical partition intersecting region 2). Proc. SPIE Vol

5 3. RESULTS 3.1. Single-step calculation method The results presented for retraction events 1-3 are the average of 4 subjects. Due to brain volume limitations, retraction event no. 4 was performed in two subjects only. Table 4 summarizes the directional components and vector displacement errors for the single-step retraction scheme. Table 4. Single-step scheme: errors (mm), ave. +/- std. (max.). Retraction Step No. Ux Uy Uz U 1* 0.3+/-0.2 (1.1) 0.4+/-0.3 (1.2) 0.3+/-0.2 (0.9) 0.3+/-0.3 (0.9) /-0.5 (2.5) 0.5+/-0.4 (2.3) 0.4+/-0.3 (1.5) 0.4+/-0.5 (1.6) /-0.7 (3.5) 0.6+/-0.5 (3.1) 0.5+/-0.4 (1.7) 0.7+/-0.7 (2.1) /-0.9 (4.5) 0.8+/-0.7 (4.1) 0.7+/-0.5 (2.3) 0.9+/-0.9 (2.8) * Step no.1 is the same for both single-step and incremental schemes. Table 5 presents how the prediction compares to the measured displacements as a percent capture for the single-step scheme. The component errors are relative to the overall vector displacement. Table 5. Single-step scheme: % capture of displacement vector. Retraction Step No. Ux Uy Uz U 1* Superimposed incremental calculation method Table 6 summarizes the directional components and vector displacement errors for the incremental retraction scheme. Table 6. Incremental scheme: errors (mm), ave. +/- std. (max.). Retraction Step No. Ux Uy Uz U 1* 0.3+/-0.2 (1.1) 0.4+/-0.3 (1.2) 0.3+/-0.2 (0.9) 0.3+/-0.3 (0.9) /-0.4 (2.3) 0.5+/-0.4 (2.4) 0.4+/-0.3 (1.4) 0.4+/-0.4 (1.3) /-0.7 (3.3) 0.6+/-0.5 (3.4) 0.5+/-0.4 (1.6) 0.6+/-0.7 (2.0) /-0.9 (4.3) 1.1+/-0.9 (4.9) 0.7+/-0.6 (2.2) 0.9+/-1.0 (2.7) Table 7 presents how the prediction compares to the measured displacements as a percent capture for the incremental scheme. Again, the component errors are relative to the overall vector displacement. Table 7. Incremental scheme: % capture of displacement vector. Retraction Step No. Ux Uy Uz U 1* Proc. SPIE Vol. 4319

6 4. DISCUSSION Although work has been completed to optimize the boundary description in each subject for improved loading predictions, the results presented herein are based upon the generalized set of boundary conditions described in section 2.3. With this sub-optimal prescription, we are able to achieve an average between 75% to 81% capture of total marker displacements using the single-step compensation scheme. The superimposed incremental approach enables between 2-4% improvement in prediction of deformation due to retraction. In this study, the majority of retractor translation was coincident with the X-axis in the CT and mesh coordinate systems. Therefore, an improvement in the x-component of a bead s trajectory had a more significant effect on the total error than the y- and z- components. As illustrated in Figure 3, it is possible that some directional components may gain error with the incremental approach, but the overall vector displacement and directional trend was improved. Figure 3. Single bead trajectory comparisons in Subject 3. A new incremental approach to tissue retraction has been developed and shown to improve data-model match in retraction experiments in the porcine brain. Incremental retraction modeling is an advance over previous single-step models, which does not incur additional computational overhead. Results in the porcine brain show that even when the overall displacement magnitudes between the two models are similar, directional trends of the displacement field are often significantly improved with the incremental method, an important outcome for application of optimized boundary conditions. ACKNOWLEDGEMENTS Supported by the National Institutes of Health (NIH) under Grant R01-NS33900 awarded by the National Institute of Neurological Disorders and Stroke. Analyze AVW software has been provided in collaboration with the Mayo Foundation. REFERENCES 1. T. Peters and B. Davey and P. Munger and R. Comeau and A. Evans and A. Olivier, Three-dimensional multimodal image-guidance for neurosurgery, IEEE Trans. Med. Imaging, 15, pp , W. E. L. Grimson, G. J. Ettlinger, S. J. White, T. Lozano-Perez, W. M. Wells III and R. Kikinis, An automated registration method for frameless stereotaxy, image guided surgery and enhanced reality visualization, IEEE Trans. Med. Imaging, 15, pp , D. W. Roberts, J. W. Strohbehn, J. F. Hatch, W. Murray and H. Kettenberger, A frameless stereotactic integration of computerized tomographic imaging and the operating microscope, Journal of Neurosurgery, 65, pp , R. L. Galloway Jr., R. J. Maciunas and C. A. Edwards, Interactive image-guided neurosurgery, IEEE Trans. Biomed. Eng., 39, pp , D. R. Sanderman and S. S. Gill, The impact of interactive image guided surgery: the Bristol experience with ISF/Elektra Viewing Wand, Acta Neurochirurgica, Suppl., 64, pp , Proc. SPIE Vol

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